。
The wedding will likely be held regardless of the weather.
Literal
Wedding [topic-は] weather [regardless-にかかわらず] will-be-held [conjecture-だろう].
A formal prediction. 天候 (てんこう, 'weather conditions') is more formal than 天気. にかかわらず ('regardless of') is a formal grammar pattern: に + 関わる (to be related) + ず (classical negative), meaning 'without being affected by.' 催される (もよおされる) is the passive of 催す ('to hold an event'), a formal verb for organized events. だろう expresses conjecture.